Well -- start by clearing the room completely -- that move alone can really help you see the whole space in a new light or form! Also: what items do you currently have to furnish it? What do you need? How about painting the room? I like the rug -- and the shelves. Clear the shelves -- and simply add some books -- and modern clean-lined glass or silver/plate items -- like bowls. For a modern touch -- add a gallery of black-and-white photos -- mat alike and frame alike too. If you plan to keep the TV in the room -- then consider angling the unit into the corner at the left-hand side of the far window. Then step back and really look at the space -- would a sofa work against the wall where the computer desk now sits? Then add a couple of armchairs and an ottoman/long coffee table. Lots of lamps too. Maybe roman blinds at the windows.

You might want to do a few calcs on how far back into the room the light will penetrate, in all the seasons. Typically with just a S facing window, there may be issues with getting enough light as the plants get further into the room, away from the window. Things like putting low plants right by the window and scaling in taller plants further back can help. And of course you mentioned adding grow lights. Also, depending on how many plants you were planning and the size of the room, humidity may become an issue. As might floor support if you were going to bring in a lot of dirt (most houses are not designed to hold a foot of dirt on the floor).

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IMO a to scale and all measurements clearly marked plan is what we need and pics of your furniture and how big is the TV. I like TV seperate from my LR if at all possible and for sure if used for gaming. Is it possible to move the TV out of the spac einto an unused bedroom maybe . Post the plan there are lots of talented people here to give advice but they all need the to scale plan It is easier to do on graph paper BTW and show all windows door ways and all measurements clearly marked